[FOM] 2,3 Turing machine proof controversy

[Alex Galicki]

On 11/11/2007, Vaughan Pratt <pratt at cs.stanford.edu> wrote:
> (My reply to Bob Hearn subsumes that to Alex.  By way of background
> information on Bob he is a Clarisworks principal who has more recently
> obtained some very nice results in collaboration with Erik Demaine and
> others.  Bob's ClarisWorks killed Microsoft Works in 1991, Bob's
> collaboration with Erik began a decade later.)
>
> Bob Hearn wrote:
> > My understanding is that this is in fact the way Smith's construction
> > works. There are no  restarts, merely a single run from an infinite
> > initial condition. Did I misunderstand?
>
> Although I still haven't figured out just where in Alex's paper it says
> this explicitly I'll go with this interpretation.  (As I understand him
> Alex is claiming that it's in the condition on page 4 of his proof,
> namely "To be precise, 'finite-length initial condition', given in this
> and future conjectures, refers to an initial condition in which only
> finitely many of the cells are relevant, and no other cells are visited
> during the evolution of that initial condition."  I'm happy to defer to
> any competent judge who's been able to read into this sentence what Alex
> claims to have been his intended meaning.  Personally I find this all
> very fuzzy.)

This is exactly why I keep asking (without much hope) if *anyone* on
this list is able to tell me what is the exact halting rule of the 2,3
machine.
The so called  'finite-length initial condition' is the only thing I
managed to find in the proof itself, but with just that rule the 2,3
machine will either always stop (for finite input) or never (for
infinite initial condition).

A.